{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,12]],"date-time":"2025-07-12T22:43:40Z","timestamp":1752360220937},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,6,30]]},"abstract":"<jats:p> In this work, we propose a class of public-key cryptosystems called multiplicative coupled cryptosystem, or MCC for short, as well as discuss its security within three different models. Moreover, we discuss a chaotic instance of MCC based on the first and the second types of Chebyshev polynomials over real numbers for these three security models. To avoid round-off errors in floating point arithmetic as well as to enhance the security of the chaotic instance discussed, the Chebyshev polynomials of the first and the second types over a finite field are employed. We also consider the efficiency of the proposed MCCs. The discussions throughout the paper are supported by practical examples. <\/jats:p>","DOI":"10.1142\/s0218127416501121","type":"journal-article","created":{"date-parts":[[2016,7,15]],"date-time":"2016-07-15T10:00:50Z","timestamp":1468576850000},"page":"1650112","source":"Crossref","is-referenced-by-count":13,"title":["Cryptanalysis of Multiplicative Coupled Cryptosystems Based on the Chebyshev Polynomials"],"prefix":"10.1142","volume":"26","author":[{"given":"Ali","family":"Shakiba","sequence":"first","affiliation":[{"name":"Department of Computer Science, Yazd University, Yazd, Iran"},{"name":"The Laboratory of Quantum Information Processing and Cryptography, Yazd University, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad Reza","family":"Hooshmandasl","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Yazd University, Yazd, Iran"},{"name":"The Laboratory of Quantum Information Processing and Cryptography, Yazd University, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohsen Alambardar","family":"Meybodi","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Yazd University, Yazd, Iran"},{"name":"The Laboratory of Quantum Information Processing and Cryptography, Yazd University, Yazd, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,7,15]]},"reference":[{"key":"S0218127416501121BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015970"},{"key":"S0218127416501121BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2005.851701"},{"key":"S0218127416501121BIB003","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1007\/3-540-46416-6_49","volume-title":"Advances in Cryptology\u2013EUROCRYPT91","author":"Biham E.","year":"1991"},{"key":"S0218127416501121BIB005","doi-asserted-by":"publisher","DOI":"10.1145\/1236463.1236468"},{"key":"S0218127416501121BIB006","volume-title":"GNU MP: The GNU Multiple Precision Arithmetic Library","author":"Granlund T.","year":"2012","edition":"5"},{"key":"S0218127416501121BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-46416-6_11"},{"key":"S0218127416501121BIB008","series-title":"Seminumerical Algorithms","volume-title":"The Art of Computer Programming","volume":"2","author":"Knuth D. 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